MathProblem 80 128 pennies and a blindfold problem

You are blindfolded before a table. On the table are a very large number of pennies. You are told 128 of the pennies are heads up and the rest are tails up. How can you create two subgroups of pennies, each with the same number of heads facing up?

Solution

注意到我们只需要关注相同数量的 \(head\). 所以不妨直接随机选取任意 128 个硬币。假设其中 \(H: x, T:128-x\).

那么剩下的一堆硬币中， \(H:128-x\).

那么只需要将第一组 \(128\) 的全部翻转即可得到 \(T: x, H:128-x\)

此时便得到答案。